static boolean containsAllEntries(Map<?,?> map1, Map<?,?> map2) {
    return map1.entrySet().containsAll(map2.entrySet());
}

static boolean containsAllKeys(Map<?,?> map1, Map<?,?> map2) {
    return map1.keySet().containsAll(map2.keySet());
}

public static void main(String[] args) {
    HashMap<String, String>
        map1 = new HashMap<>(), map2 = new HashMap<>();

    map1.put("1", "Один");  map2.put("1", "Один");
    map1.put("2", "Два");       map2.put("2", "Два");
    map1.put("3", "Три");       map1.put("3", "Три");

    map1.put("4", "Четыре");
    map1.put("5", "Пять");

    System.out.println("map1 contains all keys    from map2: " + containsAllKeys(map1, map2));
    System.out.println("map1 contains all entries from map2: " + containsAllEntries(map1, map2));

    map1.put("2", "Не два!");
    System.out.println("map1 contains all keys    from map2: " + containsAllKeys(map1, map2));
    System.out.println("map1 contains all entries from map2: " + containsAllEntries(map1, map2));

    map1.remove("2");
    System.out.println("map1 contains all keys    from map2: " + containsAllKeys(map1, map2));
    System.out.println("map1 contains all entries from map2: " + containsAllEntries(map1, map2));
}